Molecular modeling analysis for functionalized graphene/sodium alginate composite

This study examined the functionalization of graphene with easily ionizable elements, such as lithium, and subsequently its interaction with the biopolymer sodium alginate (SA), to highlight its potential for biomedical applications. Utilizing Density Functional Theory (DFT), the research comprehensively investigated the structural, electronic, and spectroscopic properties of these graphene-based composites. The electronic properties of functionalized graphene were investigated using DFT at the B3LYP/6-31G(d,p) level. Among the various configurations studied, graphene exhibited weak interaction with two lithium atoms, displaying the highest reactivity in terms of total dipole moment (TDM) at 5.967 Debye and a HOMO/LUMO energy gap (ΔE) of 0.748 eV. Electrostatic potential mapping revealed that graphene when enhanced with lithium and three units of SA, exhibited an augmented potential density on its surface, a finding corroborated by other investigated physical properties. Notably, the configuration of graphene/3SA/Li, with weak interaction occurring at two side carbons, demonstrated the highest reactivity with a TDM of 15.509 Debye and ΔE of 0.280 eV. Additionally, a shift in the spectral characteristics of graphene towards lower wavenumbers was observed as lithium and SA interacted with the graphene substrate. The PDOS plot for Graphene/3SA/Li, showed the highest contribution in the HOMO orbitals was equally from lithium, sodium, hydrogen, and oxygen, while the lowest contribution was from carbon. This computational analysis provides comprehensive insights into the functionalized graphene systems, aiding in their further development and optimization for practical biomedical use.

SA can improve its ability to encapsulate drugs, facilitating controlled and targeted drug delivery.By modifying its electronic properties, researchers can accurately determine the release kinetics of drugs from alginate-based carriers, ensuring optimal therapeutic efficacy and minimizing side effects 43,44 .Alginate-based dressings are commonly used for wound management due to their moisture-retention properties and ability to promote wound healing.Enhancing the electronic properties of SA can improve its antimicrobial activity and accelerate the healing process by providing a conducive environment for tissue regeneration while preventing infections 45,46 .
Building on these findings, the current study proposes a method to enhance both the functionality and biocompatibility of graphene.This approach involves first functionalizing graphene with a readily ionizable element like Li. Afterward, the biocompatible biopolymer SA, is introduced to further improve biocompatibility.To explore this concept, the study employed DFT at the B3LYP level to investigate the properties of graphene.The process involved sequential functionalization: graphene, then graphene-Li (various interaction schemes), and finally, the graphene-Li-SA composite.Key properties like TDM, ΔE, molecular electrostatic potential, and Infrared spectra were all calculated for these model molecules.Finally, density and projected density of states (DOS and PDOS) were plotted for better understanding of electronic properties.

Calculations details
All calculations were conducted using Gaussian 09 (G09) 47 software.This software is installed on a personal computer at the Molecular Modeling and Spectroscopy Laboratory at the National Research Centre's Centre of Excellence for Advanced Sciences.The first step involved optimizing the model molecules using DFT using a hybrid exchange-correlation functional B3LYP [48][49][50] .A split valence basis set 6-31G(d,p) was used to form B3LYP/6-31G(d,p) model for the present calculations.Following optimization of each structure, several key properties were analyzed: TDM, ΔE, and molecular electrostatic potential.Both Infrared (IR) and Raman spectra were calculated for the optimized structures, at the same level of theory.The DOS and PDOS were also studied at the same level of theory.

Building model molecules
The study employed a model molecule containing 24 carbon atoms to represent graphene (Fig. 1).They then explored various ways that Li could interact with this model of graphene.These interaction schemes are presented in Figs. 2, 3, and 4. Figure 2 depicts scenarios where Li directly replaces a carbon atom in graphene (2a), forms a complex with a single carbon (2b), or interacts weakly with one (2c) or two carbon atoms (2d).Figure 3 explores additional interactions: a single Li atom weakly bonded to five carbon atoms (3a), two Li atoms each interacting  with five carbons (3b), and three lithium atoms weakly bonded to five carbons each (3c).Finally, Fig. 4 illustrates the possibility of Li interacting along the edge of the graphene molecule.Continuing the exploration of Li interaction with graphene (presented in Figs. 2 and 3), Fig. 4 focuses on scenarios where Li interacts along the edges of the molecule.Figure 4a depicts a single Li atom forming a complex with a side carbon atom.Figures 4b through 4f illustrate various weak interactions: a single Li atom with one side carbon (4b), a single Li atom with two side carbons (4c), two Li atoms each with two side carbons (4d), three Li atoms each with two side carbons (4e), and finally, four Li atoms each with two side carbons (4f).higher TDMs generally suggest higher reactivity.The table shows that pristine graphene (without Li) has a TDM of 0.000 Debye and a ΔE of 4.035 eV.When Li is introduced and interacts with graphene in various ways (13 different schemes were investigated), both TDM and ΔE tend to change.This indicates that Li generally increases the reactivity of graphene.According to the table, the most significant increase in reactivity is observed for the structures where Li weakly interacts with either one or two carbon atoms in the middle of the graphene sheet (G/ Li and G/2Li structures).These structures exhibit the highest TDM (5.567 Debye and 5.967 Debye, respectively) and the lowest ΔE (1.070 eV and 0.748 eV, respectively).This suggests that these specific interaction schemes between Li and graphene lead to the greatest enhancement in reactivity.

Studying physical parameters of graphene/Li
Another valuable tool for understanding a molecule's reactivity is the molecular electrostatic potential (MESP) map.This map uses a color scheme to represent the potential energy of electrons at different regions of the molecule.Red indicates areas rich in electrons (negative potential), yellow represents neutral areas (zero potential), and blue indicates areas that tend to accept electrons (positive potential).MESP maps can be used to predict how a molecule might interact with its surrounding environment.Figure 5 presents the MESP maps calculated for the studied model molecules using the DFT: B3LYP/6-31g(d,p) method.Figure 5-1 depicts the MESP map of pristine graphene.As expected, the entire surface appears yellow, indicating a neutral electrostatic potential (zero charge).This is further confirmed by the side view of graphene shown in Fig. 5-2.However, when Li is introduced and interacts with graphene (Fig. 5-3), the MESP map changes significantly.In this specific case, where a single lithium atom forms a complex with a carbon atom, the area near the lithium atom appears red.This indicates a more negative potential in this region due to the presence of electron-rich Li.Continuing the analysis of MESP maps (Fig. 5), Fig. 5-4-6 depict scenarios where Li weakly interacts with graphene.In all three cases, the surface near the Li atom exhibits a red color, indicating a negative electrostatic potential due to the presence of electron-rich Li.This is consistent with the increased reactivity observed for these structures based on the data in Table 1.As shown in the table, these three interaction schemes (one Li interacting with one, two, or five carbon atoms) possess the highest calculated TDM of 5.060 Debye, 5.567 Debye, and 4.151 Debye, respectively, and the lowest ΔE of 1.272 eV, 1.070 eV, and 1.148 eV, respectively, recalling that higher TDM and lower ΔE are generally associated with greater reactivity.In contrast, Fig. 5-7-15 show yellow surfaces, indicating a neutral potential (zero charge) for various other interaction possibilities between Li and graphene.These structures likely exhibit lower reactivity compared to those presented in Fig. 5-4-6.

Vibrational spectra of graphene/Li
To confirm the stability of the optimized molecular structures, the researchers employed vibrational spectroscopy calculations.Figure 6 presents the IR spectra obtained using the DFT: B3LYP/6-31g(d,p) method.The figure compares the IR spectrum of pristine graphene to the spectra of graphene-Li composites.One important aspect to note is the absence of negative frequencies in any of the spectra.This is a positive indicator that the studied structures are optimized and stable at the chosen theoretical level (DFT: B3LYP/6-31g(d,p)).Since there is no comparison to experimental data, scaling the calculated IR spectra was not necessary.The specific assignments of the observed peaks in the spectra are provided in Table 2.
Based on the combined analysis of the IR spectra in Fig. 6 and the band assignments listed in Table 2, a key vibrational mode for pristine graphene can be identified.This mode corresponds to the stretching motion of carbon-carbon bonds, appearing in the range of 3300-3100 cm −1 .Analysis of the vibrational spectra (likely referring to Fig. 6 and Table 2) suggests that Mode 5 corresponds to a stretching motion within the molecule, detectable in the wavenumber range of 1800-1600 cm −1 .The specific peak for this mode is positioned at 3196 cm -1 .The introduction of Li to graphene influences its vibrational fingerprint, as revealed by spectral analysis (likely Table 2).This influence can be categorized into three main effects on different vibrational modes: In-plane bending: Li causes a redshift (lower wavenumber) for some graphene configurations (G_1, G_6, G_8) in this mode, while others experience a blue shift (higher wavenumber).Out-of-plane bending: Only configurations  G_7 and G_13 exhibit a redshift upon Li addition, with the rest remaining blue shifted.Stretching: Interestingly, Li induces redshifts in the stretching vibrations for pristine graphene in specific configurations (G_10-G12).
Conversely, most other configurations experience blue shifts.Li also affects the wavenumbers of certain pristine graphene modes.In some configurations (G_3, G_6, G_7, G_9, G_11, G_13), Li allows these modes to vibrate at higher wavenumbers.However, the opposite happens for the remaining configurations, where the modes are shifted to lower wavenumbers.

Physical parameters of graphene/Li/sodium alginate
The research explores the possibility of further functionalizing graphene models previously studied (G/Li and G/2Li) with SA. Figure 7 presents the model molecules for this investigation; (a) SA alone, (b) Graphene functionalized with SA (graphene/SA), (c) Graphene/SA combined with lithium weakly interacting with two carbons (graphene/SA/Li), (d) Graphene/SA combined with Li weakly interacting with two side carbons (graphene/SA/ Li).These structures were optimized using a computational method called DFT: B3LYP/6-31g(d,p).The next step involved calculating key properties like TDM and ΔE for these models.The calculated values will likely be presented in Table 3. Analysis of the calculated properties (likely from Table 3) reveals the most reactive structure to be graphene functionalized with three SA units and lithium weakly interacting with two side carbons (Fig. 7d).This structure exhibits a significantly increased TDM of 15.509 Debye compared to the other models.Additionally, ΔE is significantly reduced to 0.280 eV, indicating greater reactivity.Figure 8 depicts the MESP maps for these structures.The maps suggest that SA increases the potential density of graphene, particularly in areas close to the alginate Figure 6.IR spectrum for the studied graphene as well as graphene/Li composites.1-Graphene (G_0); 2-one carbon atom is substituted with Li atom (G-1), 3-one Li atom is complexed with carbon atom (G-2), 4-one Li atom is weakly interacted with carbon atom (G-3), 5-one Li atom is weakly interacted with two carbon atoms (G-4).6-one Li atom is weakly interacted with five carbon atoms (G-5), 7-two Li atoms each one is weakly interacted with five carbon atoms (G-6), 8-three Li atoms each one is weakly interacted with five carbon atoms (G-7).9-one Li atom is complexed with side carbon atom (G-8), 10-one Li atom is weakly interacted with one side carbon atoms (G-9), 11-one Li atom is weakly interacted with two side carbon atoms (G-10), 12-two Li atoms each one is weakly interacted with two side carbon atoms (G-11), 13-three Li atoms each one is weakly interacted with two side carbon atoms (G-12) and 14-four Li atoms each one is weakly interacted with two side carbon atoms (G-13).All structures are calculated at DFT:B3LYP/6-31g(d,p) level of theory.
Table 2. IR modes with their corresponding assignments for graphene as well as graphene interacted with Li which calculated at DFT:B3LYP/6-31g(d,p). molecules.This effect is most pronounced in the structure of three SA units, aligning well with its exceptional reactivity observed in Table 3. Table 4 presents the calculated vibrational frequencies (IR modes) and their assignments for various models using a computational method (DFT: B3LYP/6-31g(d,p)).These models include pristine graphene (G) and graphene interacting with different combinations of SA and lithium (Li); G/NaAlg: SA attached to graphene, G/2NaAlg: Graphene with two SA units, G/NaAlg/Li inner: SA, graphene, and Li (Li weakly interacting with two inner carbons of graphene), G/NaAlg/Li side: SA, graphene, and Li (Li weakly interacting with two side carbons of graphene), G/3NaAlg/Li side: Graphene with three SA units and Li (Li weakly interacting with two side carbons).The analysis of these vibrational modes suggests that introducing SA to graphene (except for the case with three SA units and side-interacting Li) does not follow a clear trend in terms of wavenumber shifts.However, graphene itself seems to be affected by the interaction with SA.In contrast, the model with three SA units and side-interacting Li (G/3NaAlg/Li side) exhibits distinct behavior.Compared to pristine graphene, the four characteristic bands in its vibrational spectrum experience a shift towards lower wavenumbers (redshift).

Global reactivity descriptors for the studied structures
This study investigated how easily molecules can lose or gain electrons (ionization potentials and electron affinities) using various methods and a specific set of conditions (6-31 + G** basis set).The results are summarized in Table 5.In general, molecules with high ionization energies are stable and less reactive, while molecules with low     51 .This part examined how adding Li atoms affected the ionization energy (IP) of graphene/SA.Surprisingly, even though Li only weakly interacts with two carbon atoms on the edge of graphene, it caused the IP to reach its highest measured value (6.871 eV).This unexpected result suggests that Li-modified graphene might be more reactive than the other components studied 52 .The electron affinity of graphene/SA when it interacts with Li atoms by various methods was also investigated.Interestingly, the calculated results reported that graphene has the highest electron affinity when Li weakly interacts with two carbon atoms on its edge.The study also calculated the electronic chemical potential (μ) of the molecules.They categorized the molecules based on their energy gap.Molecules with a large energy gap are considered "hard" and more difficult to polarize.This is because exciting electrons in these hard molecules requires a lot of energy.Conversely, molecules with a small ΔE are called "soft" and are more easily polarized 53 .Utilizing Koopman's theorem for closed-shell compounds, the electronic chemical potential (μ), chemical hardness (η), and absolute softness (S) can be formally defined, µ = −(I+A)

2
, η = 1−A 2 , and S = 1 2η , where I and A are the ionization potential and electron affinity of the compounds, respectively.
This study used two measures, absolute hardness and softness, to assess how adding Li atoms affects the stability and reactivity of graphene/SA.They found that the hardness and chemical potential of the composite changed depending on where the Li atoms were attached.This change indicates that the interaction with Li makes the graphene/SA more reactive.Parr et al. 54 developed a new way to measure a molecule's overall ability to accept electrons, called the electrophilicity index (ω).This index reflects how much energy is released when the molecule gains electrons through the most efficient possible electron transfer from a donor molecule.The definition of the electrophilicity index (ω) by Parr et al. is = µ 2 2η .The computed electrophilicity index value characterizes the biological activity of graphene/SA when interacting with Li atoms at different positions.Interestingly, Table 5 shows that when Li atoms interact with the graphene/SA composite, the electrophilicity index increases.This effect is especially pronounced when Li weakly interacts with just two carbon atoms on the edge of the graphene sheet (with a value of 71.963).This increase in electrophilicity suggests that the interaction with Li makes the composite more likely to accept electrons.Modifying SA with graphene and Li atoms could significantly improve its usefulness in medicine by making it more functional, compatible with living tissues, and adaptable for a wider range of applications [55][56][57] .

Density of states
In order to have better insight into the modification of the electronic properties of graphene following functionalization with sodium alginate (SA), Figs. 9 and 10 present the density of states (DOS) and projected density of states (PDOS), respectively, for the studied structures.DOS and PDOS can be simply identified as projecting the wavefunctions onto the atomic orbitals, and then one can compute the density of states using only certain components.PDOS is important to understand the electronic properties of graphene as a result of functionalization with SA.
As seen in Fig. 10-1, which shows the PDOS plot of SA, sodium had the highest contribution in the molecular orbitals of the SA molecule, while the lowest contribution in the molecular orbitals was from carbon atoms.In the PDOS plot of graphene shown in Fig. 10-2 both hydrogen and carbon had almost the same contribution in both HOMO and LUMO molecular orbitals.The PDOS plot of graphene/SA demonstrated in Fig. 10-3, indicates that the highest contribution in the HOMO and LUMO molecular orbitals of the graphene/SA structure is from sodium, followed by equal contributions from carbon, hydrogen, and oxygen.On the other hand, the PDOS plot of graphene/2 SA shown in Fig. 10-4, indicated that the highest contribution in the HOMO orbitals was from sodium, hydrogen and oxygen, and the lowest contribution was from the carbon atoms, while in the LUMO orbitals, the highest contribution was from sodium, followed by a much lower yet equal contribution from carbon, hydrogen and oxygen.
The introduction of lithium atoms into the graphene/SA structure either through two inner or two side carbons resulted in the same behavior in the PDOS plots shown in Fig. 10-5, -6, respectively, where the highest contribution in the HOMO orbitals was offered equally by lithium, sodium, hydrogen, and oxygen, while the lowest contribution was offered by carbon.In the LUMO orbitals, the highest contribution came from lithium, while the lowest contribution was from sodium, hydrogen, carbon and oxygen.Finally, the PDOS plot shown in Fig. 10-7, of graphene/3SA/Li, the highest contribution in the HOMO orbitals was equally from lithium, sodium, hydrogen, and oxygen, while the lowest contribution was from carbon.In the LUMO orbitals, the highest contribution came from lithium, followed by a lower contribution from sodium, hydrogen, and oxygen, while the lowest contribution was carbon.

Conclusion
In conclusion, this study has elucidated the potential of functionalized graphene, particularly through its interaction with easily ionizable elements like Li and the biopolymer SA, for biomedical applications.Employing DFT at the B3LYP/6-31G(d,p) level, we extensively explored the structural, electronic, and spectroscopic properties of these graphene-based composites.These findings reveal that graphene exhibits weak interactions with Li, showcasing heightened reactivity as evidenced by its TDM and ΔE.Electrostatic potential mapping underscored the augmented potential density on the graphene surface upon enhancement with Li and SA, supported by other investigated physical properties.Remarkably, the configuration of graphene/3SA/Li exhibited the highest reactivity, emphasizing the potential for practical biomedical applications.Additionally, spectral shifts in graphene characteristics towards lower wavenumbers were observed as a consequence of Li and SA interactions.This may be attributed to the graphene interacting with Li and alginate showing changes in its ΔE values.This finding is supported by the electronic properties indicated by both DOS and PDOS.These changes may lead to a change in the optical absorption of graphene which in turn shifts the IR bands of graphene as a result of interaction with Li and alginate.
By illustrating parameters such as TDM, ΔE, molecular electrostatic potential, DOS, PDOS, and IR spectra, this study offers a comprehensive understanding of functionalized graphene systems.

Figure 2 .
Figure 2. Model molecules of graphene interacted with Li forming G/Li in different cases (a) one carbon atom is substituted with Li atom, (b) one Li atom is complexed with carbon atom, (c) one Li atom is weakly interacted with carbon atom, (d) one Li atom is weakly interacted with two carbon atoms.All structures are calculated at DFT:B3LYP/6-31g(d,p) level of theory.

Figure 3 .
Figure 3. Model molecules of graphene interacted with Li forming G/Li in different cases (a) one Li atom is weakly interacted with five carbon atoms, (b) two Li atoms each one is weakly interacted with five carbon atoms, (c) three Li atoms each one is weakly interacted with five carbon atoms.All structures are calculated at DFT:B3LYP/6-31g(d,p) level of theory.

Figure 4 .
Figure 4. Model molecules of graphene interacted with Li forming G/Li in different cases (a) one Li atom is complexed with side carbon atom, (b) one Li atom is weakly interacted with one side carbon atoms, (c) one Li atom is weakly interacted with two side carbon atoms, d-two Li atoms each one is weakly interacted with two side carbon atoms, (e) three Li atoms each one is weakly interacted with two side carbon atoms and (f) four Li atoms each one is weakly interacted with two side carbon atoms.All structures are calculated at DFT:B3LYP/6-31g(d,p) level of theory.

Figure 5 .
Figure5.Molecular electrostatic potential maps for the studied model molecules of 1-Graphene; 2-Graphene side view, 3-one carbon atom is substituted with Li atom, 4-one Li atom is complexed with carbon atom, 5-one Li atom is weakly interacted with carbon atom, 6-one Li atom is weakly interacted with two carbon atoms.7-one Li atom is weakly interacted with five carbon atoms, 8-two Li atoms each one is weakly interacted with five carbon atoms, 9-three Li atoms each one is weakly interacted with five carbon atoms.10-one Li atom is complexed with side carbon atom, 11-one Li atom is weakly interacted with one side carbon atoms, 12-one Li atom is weakly interacted with two side carbon atoms, 13-two Li atoms each one is weakly interacted with two side carbon atoms, 14-three Li atoms each one is weakly interacted with two side carbon atoms and 15-four Li atoms each one is weakly interacted with two side carbon atoms.All structures are calculated at DFT:B3LYP/6-31g(d,p) level of theory.

Table 1
summarizes the calculated TDM and ΔE for the studied graphene models using a computational method called DFT: B3LYP/6-31g(d,p).These values are important indicators of a molecule's reactivity.Lower ΔE and